[EM] PR favoring racial minorities

[Kristofer Munsterhjelm]

Raph Frank wrote:
> On Sun, Aug 24, 2008 at 8:03 PM, Kristofer Munsterhjelm
> <km-elmet at broadpark.no> wrote:
>> As for fairness, consider the case where more than "just enough" voters
>> voted for candidate X. With your "you either get full strength or no
>> strength" scheme, some voters are going to look at the result and say "hey,
>> my vote wasn't required yet I have no power. This means my vote was wasted,
>> so I'm going to be more careful later".
> 
> With a result like
> 
> A: 40%
> B: 30%
> C: 20%
> D: 10%
> 
> Each voter for A could still be weighted as
> 
> (VA - VB)/VA = (40-30)/40 = 0.25
> 
> as only 75% of each of their votes was required to win the constituency.
> 
> Under plurality, you don't even need a majority, you just need to beat
> the 2nd best candidate.

That could work, since additional votes for A increase the weighting, 
meaning that a vote for A isn't wasted even if A wins.

>> I can see two points of view here. The first is that they got more than
>> their share by the extent that they were less than a majority, and the
>> second is that they got more than their share by the extent that they didn't
>> represent every voter. In either case, I think that there should be a
>> continuous function, but the point of view matters when considering how much
>> power should be retained in contrast to those who didn't get anything at all
>> (that is, whose candidate lost).
> 
> I don't think there is a really a way to square this.  If a party had
> 51% of every constituency, they could guarantee that they win 100% of
> the seats.

Let's look at that case, with two parties. Call them A and B. A wins 51% 
of every constituency, and that this amounts to 51 votes (thousand 
votes, whatever) out of 100. Then if there are as many top-up seats as 
there are ordinary seats, nearly all of the latter should go to B. Since 
there are two parties, by the reweighting above, the A voters would have 
strength (51-49)/51 = about 0.04. If there are 90 constituencies and 
thus 90 list seats, and all the A voters vote for A, nationally, as 
well, they'll have 51 * 90 * 0.04 = 183.60 votes worth. Meanwhile, the B 
voters have 49 * 90 = 4410 votes worth. The total is 183.60+4410 = 
4593.60, so A gets round(p * 183.60/4593.60) and B gets round(p * 
4410/4593.60) with p chosen so that the sum is 90. This turns out to be 
p = 90, A gets 4 seats and B gets 86 seats.

In total, A has 94 seats and B has 90. 94 out of 180 is 51.1% which 
isn't too bad, considering A had 51% support everywhere.

So reweighting seems to work, at least in this case. If there are fewer 
top-up seats than constituency seats, the equation would have to be 
adjusted.

> I think maybe my issue is that constituencies which elect party
> candidates are 'playing fair'.  The candidate that they elected gets
> added to the party total and thus has an effect on the national level
> seats.  A constituency which elects an independent elects an
> independent, but that has no effect on the number of seats affecting
> each party and yet they still get to decide how the party
> proportionality is decided.  This ensures national proportionality and
> then they get to add their independent representative on top of that.
> This shifts the legislature in the direction of the constituency in
> question.

Instead of a party point of view, how about an opinion point of view? 
The voters for independents also have opinions, and so their opinion 
should affect the national level (as it would explicitly if this was a 
national election). As mentioned earlier, the voters that vote for an 
independent would probably vote for the party closest to the point of 
view of that independent if they have to vote for a party. As such, the 
shift in national influence is not an artifact, since the voters do have 
the corresponding opinion. With a good normalization system (reweighting 
or quota-based), the shift won't be very large if the independent 
actually got elected, but it'll exist -- ideally to the extent that 
there was a surplus.

>> Looking at it again, the point of view that it should be with respect to
>> 100% is probably better than the one that it should be with respect to a
>> majority. Consider the case where's there unanimity towards which candidate
>> should win. Then I think the right way to treat that is as if no votes had
>> been cast at all, rather than to give those who unanimously decided to elect
>> the constituency candidate double power in contrast to those who did not
>> vote (or a hypothetical voter that'd only vote in the national election, if
>> that was possible).
> 
> Right, to allow them participate in the national vote would give them
> double power.
> 
> However, it depends on how many additional seats are being used.  If
> 1/3 of the seats were national seats, then their votes should still be
> counted but at a reduced weighting.
> 
> The voters in each constituency elect 1 and 1/3 of the seats, that
> means that if a district elects an independent locally, then their
> votes should count but with a weight of 1/4 of the votes in other
> constituencies.

Seems that we're converging on a reweighting, but from different directions.

>> If you run the national and local election as a single STV election, I think
>> you could get the result where many national candidates get a quota and
>> "outcrowd" the various regional candidates, even if those got close to a
>> quota. The problem here is that a "local plus national" election has a
>> subset constraint (on number of local and national candidates) which a plain
>> STV election doesn't have.
> 
> As long as the quota per seat is the same, then it should be OK.  In
> effect, you are just moving around votes.
> 
> Probably the easiest way to work it is to use the Hare quota
> (technically slightly lower than the Hare quota) if you are using
> PR-STV locally.
> 
> However, that is relatively minor as independents can be expected to
> hit the quota in multi-seat constituencies and thus PR-STV + MMP for
> rebalancing at the national level can be implemented without major
> issues.
> 

>> Or to put it differently, in a general case. Say that you have a situation
>> where there are n seats and n/3 top-up seats. In a district, less than 2/3
>> vote for any candidate (for example, there are ten nearly evenly matched
>> candidates). Nobody votes party-line. Who gets the seat? If the system can't
>> ensure that a candidate from the district in question gets the seat, then by
>> pigeonhole, either a national candidate or a candidate from another district
>> gets it, which is quite undesirable.
> 
> I would give it to the plurality winner (or other single seat rule
> winner) for the district.  If nobody has voted for a party, then there
> is no issue with those voters getting more power than they are
> entitled to.

I guess I should be more precise. What I meant was that the voters do 
not vote strictly according to any party's wishes on the constituency 
ballot. They do, however, vote for various (different) parties on the 
list ballot. If no candidate has a 2/3 majority in the constituency, 
that constituency still has to elect a candidate. Okay, that's fair 
enough. But now you can't use quota-based adjustment, since neither of 
the candidates met the quota, so it seems your adjustment must be based 
on the votes cast, or on relative support. In ordinary STV, you could 
just eliminate all the candidates, but the district constraint prevents 
that.

>>> Alternatively, independents might be allowed to register as mini-parties.
>>> They could be allowed to appear on the party ballots in 2-3 nearby
>>> constituencies.  As long as their 'party' receives 1 seat's worth of
>>> votes,
>>> then they are entitled to be elected in their constituency.
>> That's interesting. What would happen if it got more than one seat's worth?
>> I assume that is possible, because otherwise, the "party" would have to be
>> limited to only one constituency, in which case the top-up aspect would fail
>> to work.
> 
> I guess the candidate could specify a party for overflow votes, i.e.
> excess votes if he gets more than 1 seat's worth or all the votes if
> he doesn't get enough for a seat.  In principle, he might get elected
> on his own party list as one of the top-up seats ... though that might
> be going to far.
> 
> Anyway, I guess my concern is shown by the decoy list strategy.
> Fundamentally, MMP allows an independent to get a seat while not
> having enough votes to be entitled to that seat.  This leads to
> potential abuse or just unfairness.

Is that, in your opinion, a problem inherent to single-winner methods, 
or just to MMP as it's usually employed? If the latter, then it seems 
that the right way to compensate is to increase the representation of 
everyone else. You can't rob the independent of his only seat (he would 
then have no representation at all), so you're just left with increasing 
the relative power of the others or of their voters.